The Stress-Dependent Random Walk

Posted: 8 Jan 2016

Date Written: November 20, 2015


A log-normal random walk with parameters that are functions of market stress naturally accounts for volatility clustering and fat-tailed return distributions. Fitting this model to a stock and a bond index we find no evidence of significant misspecification despite the fact that the model has no adjustable parameters. This model can be interpreted as a stochastic volatility model without latent variables. We obtain a closed-form expression for the Value at Risk (VaR) that accommodates returns of any magnitude and discuss several other applications.

Keywords: Market model, regime-switching, stochastic volatility, value at risk, market stress, lognormal random walk, volatility clustering, fat tails

JEL Classification: C22

Suggested Citation

Gremm, Martin, The Stress-Dependent Random Walk (November 20, 2015). International Journal of Theoretical and Applied Finance, Vol. 18, No. 8, 2015, Available at SSRN:

Martin Gremm (Contact Author)

Pivot Point Advisors ( email )

Bellaire, TX 77401
United States

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